Michigan allows for publication in situations in which the defendant cannot be found to serve with process either by mail or in person.
Service of process is codified in the Michigan Court Rules at MCR 2.100. If you have attempted to serve a defendant by mail or in person and have been unable to procure his acknowledgment of receipt, then you may seek permission from the court to serve process by alternative means. The court will provide you an opportunity to seek whatever form of process you find most fitting, however, the most common form is by posting or publication according to Michigan Court Rule 2.106.
To serve by posting or publication, you must first procure the court’s permission via an order. A request for an order must be made in a verified motion dated not more than 14 days before it is filed. The motion must set forth sufficient facts to show that process cannot be served under Rule 2.105 and must state the defendant’s address or last known address, or that the address of the defendant is unknown. If the name or present address of the defendant is unknown, you must set forth facts showing diligent inquiry to ascertain it.
A hearing on the motion is not required unless the court so directs. Contact the secretary for the judge assigned to the case to find out what he requires. Once the order is granted, you must then follow Michigan Court Rule 2.106(D) regarding publication which allows for publishing a copy of the order once per week for three consecutive weeks in a newspaper in the county where the defendant resides or if his residence is unknown, then in a paper in the county where the action is pending.
For the rules on service of process in your state, search key words “Court Rules” which can typically be found via the website of the legislature or the supreme court of your state.